Definition 1 (Foward invariant set [1]})  
A set \(\mathbb {X}_r\subseteq \mathbb {X}\)  is said to be a forward or positively invariant set of the system \(x(n+1)=f(x(n))\)  if for every \(x(n) \in \mathbb {X}_r\) , \(f(x(n)) \in \mathbb {X}_r\) .

